[Merged by Bors] - feat(LightProfinite): define ℕ∪{∞} as a light profinite set

[dagurtomas]

• depends on: [Merged by Bors] - refactor(LightProfinite): redefine light profinite spaces as second countable profinite spaces #13319
• depends on: [Merged by Bors] - feat(Topology): some lemmas about continuity of maps out of one point compactifications #13355

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[github-actions]

PR summary 48a8c845a4

Import changes

No significant changes to the import graph

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Declarations diff

+ closedEmbedding_natUnionInftyEmbedding
+ continuous_iff_convergent
+ instance (X : Type*) [TopologicalSpace X] [c : CompactSpace X] [MetrizableSpace X] :
+ instance : Coe ℕ ℕ∪{∞} := optionCoe
+ instance : MetrizableSpace (OnePoint ℕ) := closedEmbedding_natUnionInftyEmbedding.metrizableSpace
+ natUnionInftyEmbedding

You can run this locally as follows

## summary with just the declaration names:
./scripts/no_lost_declarations.sh short <optional_commit>

## more verbose report:
./scripts/no_lost_declarations.sh <optional_commit>

[leanprover-community-mathlib4-bot]

This PR/issue depends on:

• [Merged by Bors] - refactor(LightProfinite): redefine light profinite spaces as second countable profinite spaces #13319
• [Merged by Bors] - feat(Topology): some lemmas about continuity of maps out of one point compactifications #13355
  By Dependent Issues (🤖). Happy coding!

[jcommelin]

Thanks 🎉

bors merge

[mathlib-bors]

Pull request successfully merged into master.

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